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Continuity of the solution to the $ L_{p}$ Minkowski problem


Author: Guangxian Zhu
Journal: Proc. Amer. Math. Soc. 145 (2017), 379-386
MSC (2010): Primary 52A40
DOI: https://doi.org/10.1090/proc/13248
Published electronically: July 25, 2016
MathSciNet review: 3565388
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Abstract: For $ p>1$ with $ p\neq n$, it is proved that the weak convergence of $ L_{p}$ surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the $ L_{p}$ Minkowski problem is continuous with respect to $ p$.


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Additional Information

Guangxian Zhu
Affiliation: Department of Mathematics, Tandon School of Engineering, New York University, 6 Metrotech Center, Brooklyn, New York 11201
Email: gz342@nyu.edu

DOI: https://doi.org/10.1090/proc/13248
Keywords: $L_{p}$ surface area measure, $L_{p}$ Minkowski problem
Received by editor(s): October 27, 2015
Received by editor(s) in revised form: March 19, 2016
Published electronically: July 25, 2016
Communicated by: Michael Wolf
Article copyright: © Copyright 2016 American Mathematical Society